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Does Treatment Lower Risk? Roman Jaeschke, MD, MSc, discusses whether treatment lowers risk.
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Does Treatment Lower Risk? Roman Jaeschke, MD, MSc, discusses whether treatment lowers risk.
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>> I'm Joan Stephenson, Editor of JAMA's Medical News and Perspectives section. Today, I have the pleasure of speaking with Dr. Roman Jaeschke about understanding the results of a clinical trial, notably whether a particular treatment lowers risk for an outcome such as death or stroke. Dr. Jaeschke, why don't you introduce yourself to our listeners? >> My name is Roman Jaeschke. I am the faculty member at McMaster University in Hamilton in the Department of Medicine and Department of Clinical Epidemiology and Biostatistics. Clinically, I work as a Critical Care/Intensive Care Unit Physician.
>> Dr. Jaeschke, what is a 2 x 2 table? And how is it useful for presenting the outcomes of a clinical trial? >> A 2 x 2 table is one of the dreaded concepts whenever we start teaching people, but it's probably also quite useful. There are two ways, in general terms, in which results could be presented. They could be presented as means. For example, after treatment, patient walks 100 meters. And before he or she could walk 50 meters. That's usually easily understood.
The other is in proportions. That means out of x patients who got Treatment A, so many were dead. And out of y patients who got Treatment B, so many were dead. Two proportions. The best way to present such results is either simply describe, for example, we had 485 patients on treatment, of which 72 died. And we had 455 patients on control treatment, of which 95 died. It's really the end of results in terms of proportion.
Those four numbers could be presented in 2 x 2 tables, which has -- it doesn't matter how we mix the rows and columns, in rows number of patients receiving treatment or receiving alternative treatment, in columns number of patients with or without the outcome of interest. In reality, all what we need to do are those two proportions, whether they are in the table or described, and I wanted to stress this is the end of the results. Everything else is manipulation of those four numbers. >> What is the difference between risk difference, which is also known as absolute risk reduction, and relative risk, which is also known as risk ratio?
>> What I find useful is, instead of talking about risk, to talk about money. Money usually interests people quite a bit. So, the example which I would like to use explaining differences between relative and absolute measures is if you go on a trip and you spend $20 for transportation and you started with $100, you spent 20% of what you had. In absolute terms, you spent $20. If you started with $40 and you spent $20, you still spent in absolute terms $20, but you have also spent 50% of what you had to start with.
If, on the other hand, you started with $1000 in your pocket and you spent $20, you still in absolute terms spent only $20, but in relative terms, you spent only 2% of what you have to start with. So, as you could see, in absolute terms, the amount remains the same. In relative terms, it may vary widely. A similar story goes with the risks. If you lower your risks from 20% to 10%, in absolute terms you lowered it by 10%, in relative terms you lowered it by half, by 50%.
If you started with 2% and lower it to 1%, in relative terms you lowered your risk by half, by 50%. We call it relative risk. At the same time, your absolute risk difference is only 1%. As you can see, those relative and absolute describe two different concepts. One concept describes in absolute terms how much risk was removed. The other describes what proportion of risks was removed. That's as close as I could get within time allotted. >> Those are really key concepts.
Can you describe the concepts of number needed to treat and number needed to harm and how these figures show the impact of a treatment? >> Again, these are concepts which result from manipulation of those two proportions and 2 x 2 table, which we had spoken about to start with. There is nothing unusual about them. Again, they are only manipulation of those numbers. For example, if we know that the risk of bad outcome on treatment is, say, 20% and the risk of bad outcome without treatment is 30%, so by treating 100 patients, you lower the risk from 30 out of 100 to 20 out of 100.
That is called our absolute risk difference. In translating those numbers a little farther, we see that treating 100 people saves us 10 events. Instead of having 30, we have 20, out of every 100 patients treated. So, one may ask a question, "How many patients we need to treat to avoid one event?" Well, if you treat 100 and you avoid 10, by making two equations, if you wish, by how many -- you are asking how many you need to treat to avoid one, and the answer is 100, 10 less, 10, 1 less.
The calculations are fairly simple. The concept appears to be appealing to at least some people in terms of understanding what the impact of intervention is. The same applies to harm because you may have certain interventions which increase harm. For example, if you anticoagulate, you can cause bleeding. If we know that bleeding risks increase from 2% to 4%, it becomes clear that by treating 100 people, you have 2 more bleeds. You can ask yourself if by treating 100, I am causing 2 bleeds, how many do I need to treat in order to risk 1 extra bleeding?
And the answer is 50. For 50, you have 1. For 100, you have 2 extra bleeds. So, again, this is simple manipulation of the same concepts about which you were talking about. They are all mathematically very simply related. In reality, what we need to know are those two proportions, risk on treatment and risk without treatment, and then look at them in a simple way. >> It seems that the same results presented in different ways may lead to different treatment decisions.
Which measure of association is the most useful in guiding clinicians' treatment decisions? >> Unfortunately, I have to disappoint you, but there is no simple answer because different measures describe slightly different concepts, which are complementary. Usually, I'm using here an example of people choosing to finance a given intervention. I will try to go for this example. When people are said that an intervention lowers the risk of a certain disease, in this situation cancer by 1/3, they are very attracted to it.
If you tell people, "We can introduce this program, and it will decrease the death from cancer by 1/3," they love it. If you tell them, on the other hand, that the risk of death with the use of certain intervention drops from roughly 0.2% to 0.1%, they are not that enthusiastic. And if you tell them that in order to save one life from this particular form of cancer, you need to perform about 10,000 of procedures requiring to come to the clinic and have certain number of false positive tests, which leads to more testing and so forth, they are quite not enthusiastic.
Well, the issue is that all these numbers describe the same procedure. The procedure was mammography. The death rate from breast cancer has dropped from 0.18% to 0.12%. You could see that the absolute difference is 0.06%, and that translates over 7-year time into about 10,000 procedures to spare one death from breast cancer. Also, 0.12 versus 0.18 means that 1/3 of deaths from breast cancer is avoided.
As you could see, people subjected to those numbers, which are coming from absolutely the same two proportion or the same 2 x 2 table, if you wish, may end up making different decisions. I'm not judging which one is right, which one is wrong, but empirically, we know that people make different decisions, when presented in data which are shown as relative or absolute or number needed to treat. I'm not saying any of them is any better than the other. It's probably worthwhile to have an idea of what which one means and definitely worthwhile to know where they are coming from, which is back to 2 x 2 table, or even easier, back to two proportions.
>> Is there anything else you would like to tell our readers about understanding treatment results? >> Well, the only other thing which comes to mind is that, depending on what we want to prove or what agenda we want to advance, we may choose different measures of association or different measures of effects, like in this case. Usually, the relative terms are much more appealing, even in this example which I used. It's easier to say that something is lowered by 1/3.
On the other hand, things like absolute risks and number needed to treat reflect the effort which has to go into an intervention. So, be cognizant of how the results may be presented to us, be cognizant of people having a different agenda, not in a negative sense, but agenda in a sense of trying to pursue certain message rather than opposite message. Again, I'm not saying any one is better than the other, but it's worthwhile to know both. >> Well, it seems to me that in order to really have a good sense of what relative risk means, you also need to know the absolute risk, as in the examples you gave.
>> Absolutely. Absolutely, 100%. >> Well, thank you, Dr. Jaeschke, for this overview of understanding whether findings from a clinical trial indicate if a particular treatment lowers risks. And for additional information about this topic, JAMAevidence subscribers can consult Chapter 7 of User's Guide to the Medical Literature. This has been Joan Stephenson of JAMA talking with Dr. Roman Jaeschke for JAMAevidence.